mull over vs cogitate

mull over and cogitate both are verbs.

Word	Noun	Adjective	Verb	Adverb
mull over	No	No	Yes	No
cogitate	No	No	Yes	No

As verbs, cogitate is a hypernym of mull over; that is, cogitate is a word with a broader meaning than mull over:

mull over: reflect deeply on a subject
cogitate: use or exercise the mind or one's power of reason in order to make inferences, decisions, or arrive at a solution or judgments

Other hypernyms of mull over include cerebrate, think.

As verbs, cogitate is a hyponym of mull over; that is, cogitate is a word with a more specific, narrower meaning than mull over:

mull over: reflect deeply on a subject
cogitate: consider carefully and deeply; reflect upon; turn over in one's mind

Other hyponyms of mull over include premeditate, theologise, theologize, introspect, bethink, question, wonder, puzzle, consider, study.

mull over (verb)	cogitate (verb)
reflect deeply on a subject	use or exercise the mind or one's power of reason in order to make inferences, decisions, or arrive at a solution or judgments
	consider carefully and deeply; reflect upon; turn over in one's mind